{"id":"https://openalex.org/W2089139137","doi":"https://doi.org/10.1137/070698178","title":"Exact de Rham Sequences of Spaces Defined on Macro-Elements in Two and Three Spatial Dimensions","display_name":"Exact de Rham Sequences of Spaces Defined on Macro-Elements in Two and Three Spatial Dimensions","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2089139137","doi":"https://doi.org/10.1137/070698178","mag":"2089139137"},"language":"en","primary_location":{"id":"doi:10.1137/070698178","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070698178","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113545293","display_name":"Joseph E. Pasciak","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joseph E. Pasciak","raw_affiliation_strings":["pasciak@math.tamu.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"pasciak@math.tamu.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panayot S. Vassilevski","raw_affiliation_strings":["vassilevski1@llnl.gov#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"vassilevski1@llnl.gov#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.531,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.83670955,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"30","issue":"5","first_page":"2427","last_page":"2446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8442396521568298},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.6669449806213379},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6395084857940674},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5566838979721069},{"id":"https://openalex.org/keywords/constant-function","display_name":"Constant function","score":0.47974908351898193},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.43991464376449585},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.43761178851127625},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4224073886871338},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41300681233406067},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3852500021457672},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3745511770248413},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13765162229537964}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8442396521568298},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6669449806213379},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6395084857940674},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5566838979721069},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.47974908351898193},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.43991464376449585},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.43761178851127625},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4224073886871338},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41300681233406067},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3852500021457672},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3745511770248413},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13765162229537964},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070698178","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070698178","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W5800307","https://openalex.org/W1523803810","https://openalex.org/W1584365460","https://openalex.org/W1964155379","https://openalex.org/W1970350533","https://openalex.org/W1985506636","https://openalex.org/W1994183034","https://openalex.org/W1997596109","https://openalex.org/W2006895912","https://openalex.org/W2009860245","https://openalex.org/W2028703925","https://openalex.org/W2033986961","https://openalex.org/W2070232376","https://openalex.org/W2075896209","https://openalex.org/W2090740209","https://openalex.org/W2106088594","https://openalex.org/W2143783905","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W2133947431","https://openalex.org/W3208509670","https://openalex.org/W2051018371","https://openalex.org/W2888635693","https://openalex.org/W2109304297","https://openalex.org/W2040445660","https://openalex.org/W2100864966","https://openalex.org/W2490196280"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"new":[3],"finite":[4],"element":[5],"spaces":[6,39,60,91],"that":[7,16,25,30,74],"can":[8,69,82],"be":[9,70,83],"constructed":[10],"for":[11,105],"agglomerates":[12,27],"of":[13,35,47,53,77,131],"standard":[14],"elements":[15,44],"have":[17,31],"certain":[18],"regular":[19],"structure.":[20],"The":[21,38,67,114],"main":[22],"requirement":[23],"is":[24],"the":[26,42,48,93,97,132],"share":[28],"faces":[29],"closed":[32],"boundaries":[33],"composed":[34],"1-d":[36],"edges.":[37],"resulting":[40,115],"from":[41,92],"agglomerated":[43],"are":[45],"subspaces":[46],"original":[49],"de":[50,79],"Rham":[51,80],"sequence":[52,76,94],"$H^1$-conforming,":[54],"$H(\\mathbf{curl})$-conforming,":[55],"$H(\\mathbf{div})$-conforming,":[56],"and":[57,104],"piecewise":[58,106],"constant":[59],"associated":[61],"with":[62],"an":[63,86],"unstructured":[64],"\u201cfine\u201d":[65],"mesh.":[66],"procedure":[68],"recursively":[71],"applied":[72],"so":[73],"a":[75],"nested":[78],"complexes":[81],"constructed.":[84],"As":[85],"illustration":[87],"we":[88],"generate":[89],"coarser":[90],"corresponding":[95],"to":[96,126,129],"lowest-order":[98,101],"N\u00e9d\u00e9lec":[99],"spaces,":[100,103,109],"Raviart\u2013Thomas":[102],"linear":[107],"$H^1$-conforming":[108],"all":[110],"in":[111,120],"three":[112],"dimensions.":[113],"V-cycle":[116],"multigrid":[117],"methods":[118],"used":[119],"preconditioned":[121],"conjugate":[122],"gradient":[123],"iterations":[124],"appear":[125],"perform":[127],"similar":[128],"those":[130],"geometrically":[133],"refined":[134],"case.":[135]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}